Six notebooks cost $8.34. How much per notebook?

69 points!!!

Amiraneli [1.4K]

Answer:

C) The solution for the given system of equations are A(0,-5) and B(-4,3)

Step-by-step explanation:

The given system of equation are : $x^{2} + y^{2} = 25\\2x + y = -5$

from equation 2, we get y = -5 - 2x .

Put the above value of y in the equation (1).

We get: $x^{2} + y^{2} = 25 \implies x^{2} + (-5-2x)^{2} = 25$

By ALGEBRAIC IDENTITY:

$(a+b)^{2} = a^{2} + b^{2} + 2ab\\ (-5-2x)^{2} = (-5)^{2} + (-2x)^{2} + 2(-5)(-2x)$

or, $x^{2} + (-5-2x)^{2} = 25 \implies x^{2} + (25 + 4x^{2} + 20x) = 25$

or, $5x^{2} + 20x = 0 \implies x(5x + 20) = 0$

⇒ x = 0 or, x = -20/5 = -4

So, the possible values for x are: x = 0 or x = -4

If x = 0, y = -5-2x = -5-2(0) = -5

and if x = -4, y = -5 -2(-4) = -5 + 8 = 3

Hence, the solution for the given system of equations are A(0,-5) and B(-4,3)

8 0

3 years ago

if the arc length of a sector in the unit circle is 3 radians, what is the measure of the angle of the sector?

velikii [3]

Well you see you take the sector and tie it 3 times the radiants which will then answer the question that you seek from within the depths of bones and minds.

3 0

3 years ago

A company is approached by a new warehouse management systems vendor to adopt a new system. The vendor claims that the warehouse

Ludmilka [50]

Answer:

a

The null hypothesis is $H_o : \mu = 180$

The alternative hypothesis is $H_a : \mu < 180$

b

The decision rule is fail to reject the null hypothesis

The conclusion

There no sufficient evidence to support the vendor claim that the warehouse management system reduces the average pick, pack, and ship time to below 3 minutes(180 seconds) per order through bin location and routing optimization

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 3 \ minutes = 180 \ seconds$

The sample size is n = 25

The excel sheet is show on the first uploaded image

The level of significance is $\alpha = 0.05$

The null hypothesis is $H_o : \mu = 180$

The alternative hypothesis is $H_a : \mu < 180$

Generally the sample mean is mathematically represented as

$\= x = \frac{156 + 136 + \cdots + 181}{25}$

=> $\= x = 173.2$

Generally the standard deviation is mathematically represented as

$\sigma = \sqrt{\frac{\sum (x_i - \= x )^2 }{n} }$

=> $\sigma = \sqrt{\frac{ (156 - 173.2 )^2 + (136 - 173.2 )^2 + \cdots + (181- 173.2 )^2 }{25} }$

=> $\sigma = 24.261$

Generally the test statistics is mathematically represented as

$t = \frac{\= x - \mu }{\frac{\sigma}{\sqrt{n} } }$

=> $t = \frac{173.2 - 180 }{\frac{24.261}{\sqrt{25} } }$

=> $z = -1.40$

Generally p-value is mathematically represented as

$p-value = P(Z < z)$

=> $p-value = P(Z < -1.40)$

From the z-table

$P(Z < -1.40) = 0.080757$

=> $p-value = 0.080757$

From the obtained value we that $p-value > \alpha$

The decision rule is fail to reject the null hypothesis

The conclusion

There no sufficient evidence to support the vendor claim that the warehouse management system reduces the average pick, pack, and ship time to below 3 minutes(180 seconds) per order through bin location and routing optimization

5 0

3 years ago

What is the solution to 0.3(12x - 16) = 0.4(12 - 3x)?

telo118 [61]

Step-by-step explanation:

The solution is one-solution

.3(12x-16)=.4(12-3x) (you do the distributive property)

3.6x-4.8=4.8-.12x (you add 1.2 to both sides)

3.6x-3.6=4.8 (You add 3.6 to both sides)

3.6x=8.4 ( You divide 3.6 both numbers)

x=0.4285...

Its a one-solution

5 0

3 years ago

Westin is on vacation and wants to purchase something for 350 euro. how much would this cost in us dollars ?

Snezhnost [94]

Answer:

418.69 usd

Step-by-step explanation:

8 0

3 years ago